Question

Ultraviolet beam of wavelength $280\, nm$ is incident on lithium surface of work function $2.5\, eV$. The maximum velocity of electron emitted from metal surface is

• A. $8.2 \times 10^{5} m / s$
• B. $10^{6} m / s$
• C. $7 \times 10^{5} m / s$
• D. $6 \times 10^{5} m / s$

Answer 1

Answer: (A)

According to Einstein's photoelectric equation
$\frac{h c}{\lambda}= \phi_{0}+\frac{1}{2} m v_{\max }^{2}$
$\therefore v_{\max } =\sqrt{\frac{2\left(\frac{h c}{\lambda}-\phi_{0}\right)}{m}}=\sqrt{\frac{2\left(\frac{1240}{280}-2.5\right)}{9.1 \times 10^{-31}}}$
( Using $ h c=1240 \,eV \,nm )$
$=\sqrt{\left(\frac{2 \times 1.9 \times 1.6 \times 10^{-19}}{9.1 \times 10^{-31}}\right)}$
$=8.2 \times 10^{5} m / s$